Investigating the Origins of Dark Matter Halo Density Profiles

Abstract

Although high-resolution N-body simulations make robust empirical predictions for the density distribution within cold dark matter halos, these studies have yielded little physical insight into the origins of the distribution. We investigate the problem using analytic and semi-analytic approaches. Simple analytic considerations suggest that the inner slope of dark matter halos cannot be steeper than alpha=2 (rho ~ r^-alpha), with alpha=1.5-1.7 being a more realistic upper limit. Our analysis suggests that any number of effects, both real (angular momentum from tidal torques, secondary perturbations) and artificial (two-body interactions, the accuracy of the numerical integrator, round-off errors), will result in shallower slopes. We also find that the halos should exhibit a well-defined relation between r_peri/r_apo and j_theta/j_r. We derive this relation analytically and speculate that it may be "universal". Using a semi-analytic scheme based on Ryden & Gunn (1987), we further explore the relationship between the specific angular momentum distribution in a halo and its density profile. For now we restrict ourselves to halos that form primarily via nearly-smooth accretion of matter, and only consider the specific angular momentum generated by secondary perturbations associated with the cold dark matter spectrum of density fluctuations. Compared to those formed in N-body simulations, our ``semi-analytic'' halos are more extended, have flatter rotation curves and have higher specific angular momentum, even though we have not yet taken into account the effects of tidal torques. Whether the density profiles of numerical halos is indeed the result of loss in angular momentum outside the central region, and whether this loss is a feature of hierarchical merging and major mergers in particular, is under investigation.Comment: 50 pages, incl. 9 figs; accepted to Ap

Density profiles of dark matter haloes on galactic and cluster scales

“…The random angular momentum is important to the particle (shell) orbits since the larger it is, the larger is the orbital ellipticity, and the shell then penetrates less to the center, resulting in a flattening of the inner density profile. In several of the previously quoted papers (even Williams et al 2004), only the random angular momentum was taken into consideration, while we also take account of ordered angular momentum, dynamical friction, and adiabatic contraction. The collapse starts from the innermost shell, the one adjacent to the core.…”

“…These galaxies are characterized by high values of λ, since, as shown in Boissier et al (2002), 35% of all galaxies (in number) with 0.06 < λ < 0.21 are LSBs. According to several analytical papers (Nusser 2001;Hiotelis 2002;Le Delliou & Henriksen 2003;Ascasibar et al 2004;Williams et al 2004), one therefore expects that these objects should typically have shallower density cusps. Moreover the cores of these galaxies are also much less dense than the simulations indicate.…”

“…The reason is that the point of force of numerical simulations (namely to capture the full extent of the complexity of a non-linear process) is also their weakness: numerical simulations yield little physical insight beyond empirical findings precisely because they are so rich in dynamical processes, which are hard to disentangle and interpret in terms of the underlying physics. Analytical and semi-analytical models are more flexible than N-body simulations (see Williams et al 2004). So even if analytical models such as SIM consider collapse and virialization of halos that are spherically symmetric, that have suffered no major mergers, and that have suffered quiescent accretion, their investigation can provide important results.…”

“…The model is an extension of the Williams et al (2004) model that take account of ordered angular momentum, dynamical friction, and adiabatic contraction. This model derives the initial shape of proto-haloes from the fluctuation spectrum at high redshifts, and haloes are endowed with secondary perturbations, which impart random motions to halo particles, as in Williams et al (2004), and ordered angular momentum. The statistical properties of the secondary perturbations are derived from the same fluctuation power spectrum, and therefore their effects on particle random velocities are treated self-consistently.…”

Evolution of spherical overdensities in holographic dark energy models

“…To study the non-linear evolution of cosmic structures a popular analytical model, the spherical collapse model, was first introduced by Gunn & Gott (1972) and extended and improved by several following works (Fillmore & Goldreich 1984;Bertschinger 1985;Hoffman & Shaham 1985;Ryden & Gunn 1987;Avila-Reese et al 1998;Subramanian et al 2000;Ascasibar et al 2004;Williams et al 2004). Recently the formalism of the spherical collapse model was extended to include shear and rotation (del Popolo et al 2013a,b,c) and non-minimally ⋆ malekjani@basu.ac.ir coupled models (Pace et al 2014).…”